
# Packages and Data Import
from tkinter import OFF
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib
from matplotlib import pyplot as plt
from scipy.stats import zscore, norm, linregress
from sklearn.decomposition import PCA
from mpl_toolkits.mplot3d import Axes3D

import warnings
warnings.filterwarnings("ignore", category=FutureWarning)

plt.style.use('default')

pd.set_option('display.max_columns', 1000)  # or 1000
pd.set_option('display.max_rows', 1000)  # or 1000
pd.set_option('display.max_colwidth', None)  # or 199

sns.set_palette('bright')
# sns.set()

# Importing a dataframe 
df = pd.read_csv(r"https://raw.githubusercontent.com/lucasabdalah/Exploratory-Data-Analisys/hw1-report/code/hw1/breast-cancer.csv")


# Check if tha data is ok
df.tail(5) # Last 5 rows of a dataframe


print("N = {} Observations\n".format(len(df.axes[0])))
print("D = {} Predictor variables\n".format(len(df.columns)))
print("Predictor Names:\n{}\n".format(df.columns.to_list()))
print("Class-Distribution:\n{}".format(df["diagnosis"].value_counts()))

N = 569 Observations

D = 32 Predictor variables

Predictor Names:
['id', 'diagnosis', 'radius_mean', 'texture_mean', 'perimeter_mean', 'area_mean', 'smoothness_mean', 'compactness_mean', 'concavity_mean', 'concave points_mean', 'symmetry_mean', 'fractal_dimension_mean', 'radius_se', 'texture_se', 'perimeter_se', 'area_se', 'smoothness_se', 'compactness_se', 'concavity_se', 'concave points_se', 'symmetry_se', 'fractal_dimension_se', 'radius_worst', 'texture_worst', 'perimeter_worst', 'area_worst', 'smoothness_worst', 'compactness_worst', 'concavity_worst', 'concave points_worst', 'symmetry_worst', 'fractal_dimension_worst']

Class-Distribution:
B    357
M    212
Name: diagnosis, dtype: int64


df = df.drop('id', axis = 1) # Let the data anonymous and delete the id (meaningless)
numeric_columns = df.select_dtypes(include=[np.number]).columns # retrieving only numerical columns from dataframe


df.head()


# Checking if there are missing values 
df.isnull() is True

False


n_of = {"rows": 3, "cols": 10};

fig1, axes1 = plt.subplots(n_of["rows"], n_of["cols"], figsize=(30,10));

i = 0
for ii in range(n_of["rows"]):
        for jj in range(n_of["cols"]):
                # Plot Histogram
                ax = axes1[ii]
                _, bins, _ = ax[jj].hist(df[numeric_columns[i]], bins = 30, alpha = 0.5, color = "tab:green")
                ax[jj].grid('on')
                ax[jj].set_xlabel(numeric_columns[i], fontsize = 8)           
                # Plot Normal - Best Fit Line
                mu, sigma = norm.fit(df[numeric_columns[i]])
                best_fit_line = norm.pdf(bins, mu, sigma)
                ax[jj].plot(bins, best_fit_line, 'r--', linewidth=2)
                
                i += 1

fig1.suptitle('Unconditional Histogram')
fig1.tight_layout()
plt.show()

# fig1.savefig(r"figures/2-1-unconditional-histogram.pdf")
# fig1.savefig(r"figures/2-1-unconditional-histogram.png")


df.describe() # retrieve descriptive statistics


print("Predictor Mean: \n{}\n".format(df.mean(axis = 0).to_dict()))
print("Predictor Standard Deviation: \n{}\n".format(df.std(axis = 0).to_dict()))
print("Predictor Skewness: \n{}\n".format(df.skew(axis = 0).to_dict()))

Predictor Mean: 
{'radius_mean': 14.127291739894563, 'texture_mean': 19.28964850615117, 'perimeter_mean': 91.96903339191566, 'area_mean': 654.8891036906857, 'smoothness_mean': 0.096360281195079, 'compactness_mean': 0.10434098418277686, 'concavity_mean': 0.08879931581722322, 'concave points_mean': 0.048919145869947236, 'symmetry_mean': 0.181161862917399, 'fractal_dimension_mean': 0.06279760984182778, 'radius_se': 0.4051720562390161, 'texture_se': 1.2168534270650269, 'perimeter_se': 2.8660592267135288, 'area_se': 40.33707908611603, 'smoothness_se': 0.007040978910369071, 'compactness_se': 0.025478138840070306, 'concavity_se': 0.031893716344463946, 'concave points_se': 0.011796137082601056, 'symmetry_se': 0.020542298769771532, 'fractal_dimension_se': 0.0037949038664323383, 'radius_worst': 16.269189806678394, 'texture_worst': 25.677223198594014, 'perimeter_worst': 107.2612126537786, 'area_worst': 880.5831282952545, 'smoothness_worst': 0.13236859402460469, 'compactness_worst': 0.25426504393673144, 'concavity_worst': 0.27218848330404205, 'concave points_worst': 0.11460622319859404, 'symmetry_worst': 0.29007557117750454, 'fractal_dimension_worst': 0.08394581722319855}

Predictor Standard Deviation: 
{'radius_mean': 3.524048826212078, 'texture_mean': 4.301035768166949, 'perimeter_mean': 24.2989810387549, 'area_mean': 351.9141291816527, 'smoothness_mean': 0.014064128137673616, 'compactness_mean': 0.0528127579325122, 'concavity_mean': 0.0797198087078935, 'concave points_mean': 0.03880284485915359, 'symmetry_mean': 0.027414281336035712, 'fractal_dimension_mean': 0.007060362795084459, 'radius_se': 0.2773127329861041, 'texture_se': 0.5516483926172023, 'perimeter_se': 2.021854554042107, 'area_se': 45.49100551613178, 'smoothness_se': 0.003002517943839067, 'compactness_se': 0.017908179325677377, 'concavity_se': 0.030186060322988394, 'concave points_se': 0.006170285174046866, 'symmetry_se': 0.008266371528798399, 'fractal_dimension_se': 0.0026460709670891942, 'radius_worst': 4.833241580469324, 'texture_worst': 6.146257623038323, 'perimeter_worst': 33.60254226903635, 'area_worst': 569.3569926699492, 'smoothness_worst': 0.022832429404835458, 'compactness_worst': 0.15733648891374194, 'concavity_worst': 0.20862428060813235, 'concave points_worst': 0.0657323411959421, 'symmetry_worst': 0.06186746753751869, 'fractal_dimension_worst': 0.01806126734889399}

Predictor Skewness: 
{'radius_mean': 0.9423795716730992, 'texture_mean': 0.6504495420828159, 'perimeter_mean': 0.9906504253930081, 'area_mean': 1.6457321756240424, 'smoothness_mean': 0.45632376481955844, 'compactness_mean': 1.1901230311980404, 'concavity_mean': 1.4011797389486722, 'concave points_mean': 1.1711800812336282, 'symmetry_mean': 0.7256089733641999, 'fractal_dimension_mean': 1.3044888125755076, 'radius_se': 3.0886121663847574, 'texture_se': 1.646443808753053, 'perimeter_se': 3.443615202194899, 'area_se': 5.447186284898394, 'smoothness_se': 2.314450056636759, 'compactness_se': 1.9022207096378565, 'concavity_se': 5.110463049043661, 'concave points_se': 1.4446781446974786, 'symmetry_se': 2.1951328995478216, 'fractal_dimension_se': 3.923968620227413, 'radius_worst': 1.1031152059604372, 'texture_worst': 0.49832130948716474, 'perimeter_worst': 1.1281638713683722, 'area_worst': 1.8593732724433467, 'smoothness_worst': 0.4154259962824678, 'compactness_worst': 1.4735549003297956, 'concavity_worst': 1.1502368219460262, 'concave points_worst': 0.49261552688550875, 'symmetry_worst': 1.433927765189328, 'fractal_dimension_worst': 1.6625792663955146}


# Data Preprocessing: apply z-score 
df_Zscore = df.copy()
df_Zscore[numeric_columns] = df_Zscore[numeric_columns].apply(zscore);
# Split dataset by class
df_Zscore_Benign = df_Zscore[df_Zscore['diagnosis']=='B'];
df_Zscore_Malignant = df_Zscore[df_Zscore['diagnosis']=='M'];


fig2, axes2 = plt.subplots(n_of["rows"], n_of["cols"], figsize=(30,10))

i = 0
for ii in range(n_of["rows"]):
        for jj in range(n_of["cols"]):
                # Histogram of Beningn and Malignant 
                ax = axes2[ii]
                ax[jj].hist(df_Zscore_Benign[numeric_columns[i]], bins = 30, color="tab:blue", alpha = 0.5, label = 'B')
                ax[jj].hist(df_Zscore_Malignant[numeric_columns[i]], bins = 30, color="tab:orange", alpha = 0.5, label = 'M')
                ax[jj].set_xlabel(numeric_columns[i], fontsize = 8)
                i += 1

fig2.suptitle('Histogram by Class (Z-score Normalization)')
plt.legend(loc = 'upper right', bbox_to_anchor = (1.75, 1.85), frameon = True, shadow = True)
plt.show()
# fig2.savefig(r"figures/3-1-conditional-histogram.pdf")
# fig2.savefig(r"figures/3-1-conditional-histogram.png")


print("Mean\n")
print("- Benign: \n{}\n".format(df_Zscore_Benign.mean(axis = 0).to_dict()))
print("- Malignant: \n{}\n".format(df_Zscore_Malignant.mean(axis = 0).to_dict()))

print("Standard Deviation\n")
print("- Benign: \n{}\n".format(df_Zscore_Benign.std(axis = 0).to_dict()))
print("- Malignant: \n{}\n".format(df_Zscore_Malignant.std(axis = 0).to_dict()))

print("Skewness\n")
print("- Benign: \n{}\n".format(df_Zscore_Benign.skew(axis = 0).to_dict()))
print("- Malignant: \n{}\n".format(df_Zscore_Malignant.skew(axis = 0).to_dict()))

Mean

- Benign: 
{'radius_mean': -0.5625662115112122, 'texture_mean': -0.3199453412702914, 'perimeter_mean': -0.572281287623049, 'area_mean': -0.5463490052176833, 'smoothness_mean': -0.2763093742433902, 'compactness_mean': -0.4596939513531881, 'concavity_mean': -0.5366207431743413, 'concave points_mean': -0.5984652639994948, 'symmetry_mean': -0.2546850111800504, 'fractal_dimension_mean': 0.009892766381598653, 'radius_se': -0.43703817046831916, 'texture_se': 0.0063986193706725685, 'perimeter_se': -0.42856678023048056, 'area_se': -0.4224753021705948, 'smoothness_se': 0.05164311063860298, 'compactness_se': -0.225787722320827, 'concavity_se': -0.19552632667253503, 'concave points_se': -0.31444090973929467, 'symmetry_se': 0.005025720825120726, 'fractal_dimension_se': -0.060086211387773585, 'radius_worst': -0.5983419192968013, 'texture_worst': -0.352093219999986, 'perimeter_worst': -0.6033203268439074, 'area_worst': -0.5654918450100106, 'smoothness_worst': -0.32478442482814657, 'compactness_worst': -0.45542829422653364, 'concavity_worst': -0.508301266785302, 'concave points_worst': -0.6115287566044159, 'symmetry_worst': -0.32079995478401957, 'fractal_dimension_worst': -0.24957867724814478}

- Malignant: 
{'radius_mean': 0.9473402712712391, 'texture_mean': 0.5387758812900668, 'perimeter_mean': 0.9637000928369271, 'area_mean': 0.9200311078429861, 'smoothness_mean': 0.46529455945702697, 'compactness_mean': 0.7741072671372081, 'concavity_mean': 0.9036490816662274, 'concave points_mean': 1.007792920980282, 'symmetry_mean': 0.4288799480720667, 'fractal_dimension_mean': -0.016659045274671772, 'radius_se': 0.7359557870622164, 'texture_se': -0.010775033562878173, 'perimeter_se': 0.7216902855767995, 'area_se': 0.7114324663910482, 'smoothness_se': -0.08696504951878013, 'compactness_se': 0.3802180040968654, 'concavity_se': 0.32925895576459974, 'concave points_se': 0.5295066263062654, 'symmetry_se': -0.008463124219660547, 'fractal_dimension_se': 0.10118291257280738, 'radius_worst': 1.0075852131554608, 'texture_worst': 0.5929116959433726, 'perimeter_worst': 1.0159686636003527, 'area_worst': 0.9522669276819521, 'smoothness_worst': 0.5469247153945668, 'compactness_worst': 0.7669240615041141, 'concavity_worst': 0.8559601520865707, 'concave points_worst': 1.0297913495649846, 'symmetry_worst': 0.5402150181976186, 'fractal_dimension_worst': 0.4202810744225816}

Standard Deviation

- Benign: 
{'radius_mean': 0.5056905839209924, 'texture_mean': 0.9296923108054224, 'perimeter_mean': 0.48635071823073406, 'area_mean': 0.38192634370043366, 'smoothness_mean': 0.9568960357257115, 'compactness_mean': 0.6396115695856717, 'concavity_mean': 0.5454149509785584, 'concave points_mean': 0.41035074835329294, 'symmetry_mean': 0.9056807010411009, 'fractal_dimension_mean': 0.9565060550454667, 'radius_se': 0.4062873577376952, 'texture_se': 1.0689746424954234, 'perimeter_se': 0.3817523613510809, 'area_se': 0.1945715041425255, 'smoothness_se': 1.0202445815507457, 'compactness_se': 0.913878438956671, 'concavity_se': 1.0914707145051077, 'concave points_se': 0.9259940996167308, 'symmetry_se': 0.8473725945267777, 'fractal_dimension_se': 1.111385257502007, 'radius_worst': 0.4103066091943269, 'texture_worst': 0.8946563846030345, 'perimeter_worst': 0.40291574387948953, 'area_worst': 0.28759702261305176, 'smoothness_worst': 0.87730808633975, 'compactness_worst': 0.5863934609180007, 'concavity_worst': 0.6734175388616728, 'concave points_worst': 0.5450721979321205, 'symmetry_worst': 0.6753387375556162, 'fractal_dimension_worst': 0.7649624441323942}

- Malignant: 
{'radius_mean': 0.9099732766874362, 'texture_mean': 0.8795080208082193, 'perimeter_mean': 0.9001975452068824, 'area_mean': 1.046453363769089, 'smoothness_mean': 0.897270651663947, 'compactness_mean': 1.0231429009310478, 'concavity_mean': 0.9418654932498716, 'concave points_mean': 0.8866399980850427, 'symmetry_mean': 1.0090511004651688, 'fractal_dimension_mean': 1.073596210799654, 'radius_se': 1.2453167034440826, 'texture_se': 0.8766511953963066, 'perimeter_se': 1.271508723672301, 'area_se': 1.3499208003891718, 'smoothness_se': 0.9635157086944846, 'compactness_se': 1.027651576138213, 'concavity_se': 0.7163053705225972, 'concave points_se': 0.8949695165764129, 'symmetry_se': 1.2186416312924044, 'fractal_dimension_se': 0.7721993335307876, 'radius_worst': 0.8870523998562343, 'texture_worst': 0.8850241016240249, 'perimeter_worst': 0.877403085497036, 'area_worst': 1.0511750965295765, 'smoothness_worst': 0.9586836841976226, 'compactness_worst': 1.0838038606265503, 'concavity_worst': 0.870782771672425, 'concave points_worst': 0.7051100752770995, 'symmetry_worst': 1.2082387389066807, 'fractal_dimension_worst': 1.1943709357470584}

Skewness

- Benign: 
{'radius_mean': -0.08379911084596989, 'texture_mean': 0.9813438242995706, 'perimeter_mean': -0.0646840376021128, 'area_mean': 0.34226544208948545, 'smoothness_mean': 0.6634478209195397, 'compactness_mean': 1.2124425769205047, 'concavity_mean': 3.473264085577407, 'concave points_mean': 0.9249653214200644, 'symmetry_mean': 0.6589430383689463, 'fractal_dimension_mean': 1.6506633823954264, 'radius_se': 1.5039240750600325, 'texture_se': 1.6545037096614243, 'perimeter_se': 1.187739545054796, 'area_se': 1.6461421572692583, 'smoothness_se': 1.5084961295041153, 'compactness_se': 2.2122920668499777, 'concavity_se': 6.327025092111964, 'concave points_se': 2.147108644423603, 'symmetry_se': 1.3778151210582004, 'fractal_dimension_se': 4.335433003815259, 'radius_worst': -0.03158576045510419, 'texture_worst': 0.7218162084498397, 'perimeter_worst': 0.008736362474584336, 'area_worst': 0.3674540642323875, 'smoothness_worst': 0.34115599277139497, 'compactness_worst': 1.0961220011061004, 'concavity_worst': 2.5537146897238094, 'concave points_worst': 0.11226460965119833, 'symmetry_worst': 0.23465495205739909, 'fractal_dimension_worst': 1.4157321823622857}

- Malignant: 
{'radius_mean': 0.5019020231808626, 'texture_mean': 0.703542624985751, 'perimeter_mean': 0.6049305890212234, 'area_mean': 1.1176681747743724, 'smoothness_mean': 0.4797513061122113, 'compactness_mean': 0.836768077433169, 'concavity_mean': 0.9016281304158735, 'concave points_mean': 0.7390917371569512, 'symmetry_mean': 0.8119599523202241, 'fractal_dimension_mean': 0.8947663696043217, 'radius_se': 2.519402346895163, 'texture_se': 1.536327589425506, 'perimeter_se': 2.810137262533995, 'area_se': 4.345029138933036, 'smoothness_se': 3.958781820813507, 'compactness_se': 1.857940033901191, 'concavity_se': 1.6239704141897409, 'concave points_se': 1.437999217337326, 'symmetry_se': 2.5195810681208375, 'fractal_dimension_se': 1.6720109441893805, 'radius_worst': 0.6314687485918912, 'texture_worst': 0.5398839789019378, 'perimeter_worst': 0.7481792411930523, 'area_worst': 1.3077621628765124, 'smoothness_worst': 0.43734426447515007, 'compactness_worst': 1.1015505134134165, 'concavity_worst': 0.9126522908541799, 'concave points_worst': -0.09280877923976935, 'symmetry_worst': 1.1490013924496654, 'fractal_dimension_worst': 1.363200467396273}


# n_rows, n_cols = 2, 2
# fig4, axes4 = plt.subplots(n_rows, n_cols, figsize=(5,5))

n_rows, n_cols = 30, 30
fig4, axes4 = plt.subplots(n_rows, n_cols, figsize=(100,100))

# 2 minutes to process with I7 10th gen + 20 Gb RAM setup
for ii in range(n_rows):
  for jj in range(n_cols):
    ax = axes4[ii]
    ax[jj].set_xlabel(numeric_columns[jj])
    ax[jj].set_ylabel(numeric_columns[ii])
    
    if ii > jj:
      ax[jj].scatter(df_Zscore_Benign[numeric_columns[jj]], df_Zscore_Benign[numeric_columns[ii]], alpha = 0.5, label = 'B')
      ax[jj].scatter(df_Zscore_Malignant[numeric_columns[jj]], df_Zscore_Malignant[numeric_columns[ii]], alpha = 0.5, label = 'M')
    
    if ii == jj:
      ax[jj].text(0.25, 0.5, "{}".format(numeric_columns[ii]), style ='normal', fontsize = 10, color ="black")
      ax[jj].axis('off')
    if ii < jj:
      ax[jj].axis('off')
    else:
      pass

plt.tight_layout()
fig4.suptitle('Scatter Plot (Z-score Normalization)')
fig4.legend({'B', 'M'}, loc = 'upper center', bbox_to_anchor = (0.5, 0.95), ncol = 2, frameon = True, shadow = True)
plt.show()
# fig4.savefig(r"figures/4-1-scatter-plot.pdf")
# fig4.savefig(r"figures/4-1-scatter-plot.png")


n_rows, n_cols = 3, 10
fig5, axes5 = plt.subplots(n_rows, n_cols, figsize = (20, 10))  

i = 0
for ii in range(n_rows):
    for jj in range(n_cols): 
        ax5 = axes5[ii]
        df_Zscore.boxplot(numeric_columns[i], by = 'diagnosis', ax = ax5[jj], patch_artist = True)
        ax5[jj].findobj(matplotlib.patches.Patch)[0].set_facecolor("tab:blue")
        ax5[jj].findobj(matplotlib.patches.Patch)[1].set_facecolor("tab:orange")
        i += 1

fig5.suptitle('Scatter Plot (Z-score Normalization)')
plt.tight_layout()
plt.show()
# fig5.savefig(r"figures/4-2-box-plot.pdf")
# fig5.savefig(r"figures/4-2-box-plot.png")


fig6 = plt.figure(figsize=(12, 12))
plt.matshow(df.corr(), fignum=fig6.number, cmap="coolwarm", interpolation='none')
plt.xticks(range(df[numeric_columns].shape[1]),df[numeric_columns].columns, rotation=90)
plt.yticks(range(df[numeric_columns].shape[1]), df[numeric_columns].columns)
cb = plt.colorbar()
plt.clim(-1,1)
cb.ax.tick_params(labelsize=12)
plt.title('Correlation Matrix', fontsize=16)

# Gridlines based on minor ticks
ax = plt.gca();
ax.set_xticks(np.arange(-.5, 30, 1), minor=True)
ax.set_yticks(np.arange(-.5, 30, 1), minor=True)
ax.grid(which='minor', color='k', linestyle='-', linewidth=2)
plt.show()

# fig6.savefig(r"figures/4-3-correlation.pdf")
# fig6.savefig(r"figures/4-3-correlation.png")


fig7 = plt.figure(figsize=(8, 8))
thre = 0.9;
plt.matshow((df.corr() > thre) + (df.corr() < -thre), fignum=fig7.number, cmap="coolwarm")
plt.clim(-1,1)
plt.title('Highlight Great Correlations $(|p|\geq {})$'.format(thre), fontsize=16)

# Gridlines based on minor ticks
ax = plt.gca();
ax.set_xticks(np.arange(0, 30, 1))
ax.set_yticks(np.arange(0, 30, 1))
ax.set_xticklabels(np.arange(1, 31, 1))
ax.set_yticklabels(np.arange(1, 31, 1))
ax.set_xticks(np.arange(-.5, 30, 1), minor=True)
ax.set_yticks(np.arange(-.5, 30, 1), minor=True)
ax.grid(which='minor', color='k', linestyle='-', linewidth=2)
fig7.savefig(r"figures/4-3-correlation-90p.pdf")
fig7.savefig(r"figures/4-3-correlation-90p.png")

fig8 = plt.figure(figsize=(8, 8))
thre = 0.95;
plt.matshow((df.corr() > thre) + (df.corr() < -thre), fignum=fig8.number, cmap="coolwarm")
plt.clim(-1,1)
plt.title('Highlight Great Correlations $(|p|\geq {})$'.format(thre), fontsize=16)

# Gridlines based on minor ticks
ax = plt.gca();
ax.set_xticks(np.arange(0, 30, 1))
ax.set_yticks(np.arange(0, 30, 1))
ax.set_xticklabels(np.arange(1, 31, 1))
ax.set_yticklabels(np.arange(1, 31, 1))
ax.set_xticks(np.arange(-.5, 30, 1), minor=True)
ax.set_yticks(np.arange(-.5, 30, 1), minor=True)
ax.grid(which='minor', color='k', linestyle='-', linewidth=2)
fig8.savefig(r"figures/4-3-correlation-95p.pdf")
fig8.savefig(r"figures/4-3-correlation-95p.png")
plt.show()


fig9 = plt.figure(figsize=(5, 5))

# Observe the variance retained in each PC
n_PCA = 2
pca = PCA(n_components=n_PCA) 
pca.fit_transform(df_Zscore[numeric_columns])

screeplot = np.zeros(n_PCA+1)
screeplot[1:n_PCA+1] = np.cumsum(pca.explained_variance_ratio_)

plt.axhline(y=0.95, color="black", linestyle="--")
plt.plot(np.linspace(1,len(pca.explained_variance_ratio_), n_PCA), screeplot[1:], color = "tab:red", marker = "o")
plt.bar(range(1,len(pca.explained_variance_ratio_)+1),pca.explained_variance_ratio_, color = "tab:blue", alpha = 0.5)


plt.xticks(range(1, len(pca.explained_variance_ratio_)+1))
plt.ylim([0, 1])
plt.xlabel('PCA Component')
plt.ylabel('Normalized Variance')
plt.grid('minor')
plt.legend(["$\sigma = 0.95$","Cumulative Variance"], loc = 'center', ncol= 3, bbox_to_anchor = (0.5, 0.8), frameon = True, shadow = True)
plt.title('Feature Explained Normalized Variance')
plt.show()
# fig9.savefig(r"figures/5-1-PCA-2PC-variance.pdf")
# fig9.savefig(r"figures/5-1-PCA-2PC-variance.png")


fig10 = plt.figure(figsize=(6, 4))

 # Observe the variance retained in each PC
n_PCA = 10
pca = PCA(n_components=n_PCA) 
pca.fit_transform(df_Zscore[numeric_columns])

screeplot = np.zeros(n_PCA+1)
screeplot[1:n_PCA+1] = np.cumsum(pca.explained_variance_ratio_)

plt.axhline(y=0.95, color="black", linestyle="--")
plt.plot(np.linspace(0,len(pca.explained_variance_ratio_), n_PCA), screeplot[0:-1], color = "tab:red", marker = "o")
plt.bar(range(1,len(pca.explained_variance_ratio_)+1),pca.explained_variance_ratio_, color = "tab:blue", alpha = 0.5)

plt.xticks(range(1, len(pca.explained_variance_ratio_)+1))
plt.yticks(np.linspace(0, 1, n_PCA+1))
plt.xlim([0, n_PCA+0.5])
plt.xlabel('PCA Component')
plt.ylabel('Normalized Variance')
plt.grid('minor')
plt.title('Feature Explained Normalized Variance')
plt.legend(["$\sigma = 0.95$","Cumulative Variance"])
plt.show()
# fig10.savefig(r"figures/5-1-PCA-10PC-variance.pdf")
# fig10.savefig(r"figures/5-1-PCA-10PC-variance.png")


# Observe the variance retained in each PC
n_PCA = 2
pca = PCA(n_components=n_PCA) 
pca_features = pca.fit_transform(df_Zscore[numeric_columns])

pca_df = pd.DataFrame(data=pca_features, columns=['PC1', 'PC2'])
pca_df['diagnosis'] = df_Zscore["diagnosis"]

# Create the scaled PCA dataframe
pca_df_scaled = pca_df.copy()

scaler_df = pca_df[['PC1', 'PC2']]
scaler = 1 / (scaler_df.max() - scaler_df.min())
 
for index in scaler.index:
    pca_df_scaled[index] *= scaler[index]

fig11 = sns.lmplot(
  x='PC1', 
  y='PC2', 
  data=pca_df_scaled, 
  hue='diagnosis', 
  scatter_kws={'alpha':0.5}, 
  fit_reg=False, 
  legend=False, 
  hue_order=["B", "M"]
)

plt.title('PCA - Normalized 2D Projection')
plt.legend(["B", "M"], loc = 'center', ncol= 1, bbox_to_anchor = (0.9, 0.9), frameon = True, shadow = True)
plt.grid("on")
plt.tight_layout()
plt.show()
# fig11.savefig(r"figures/5-2-PCA-2D-scatter.pdf")
# fig11.savefig(r"figures/5-2-PCA-2D-scatter.png")


fig12 = plt.figure(figsize=(6, 4))

# Plot the loadings on a scatterplot
for i, varnames in enumerate(numeric_columns):
    plt.scatter(pca.components_[0][i], pca.components_[1][i], marker = "s", s=50)
    # plt.text(pca.components_[0][i], pca.components_[1][i], varnames,fontsize=10)
 
# Define the axes
slope, intercept, r, p, std_err = linregress(pca.components_[0], pca.components_[1])
x = slope * np.linspace(-0.05, 0.22, 10) + intercept
y = np.linspace(-0.05, 0.22, 10)
plt.plot(x, y, color = "tab:red", linestyle='--')

plt.axhline(y=0, color = "black", linestyle=':', label='_nolegend_')
plt.axvline(x=0, color = "black", linestyle=':', label='_nolegend_')

plt.xlabel('PC1')
plt.ylabel('PC2')
plt.legend(
    ["Linear Regression",
    "Radius", 
    "Texture", 
    "Perimeter", 
    "Area", 
    "Smoothness", 
    "Compactness", 
    "Concavity", 
    "Concave Points", 
    "Symetry", 
    "Fractal Dimension"],
    title = "Predictor Type", ncol= 1, bbox_to_anchor = (1.01, 1.0), frameon = True, shadow = True)

plt.grid("on")
plt.tight_layout()
plt.title('PCA - 2D Loading')
plt.show()

# fig12.savefig(r"figures/5-2-PCA-2D-loading.pdf")
# fig12.savefig(r"figures/5-2-PCA-2D-loading.png")


# Observe the variance retained in each PC
n_PCA = 2
pca = PCA(n_components=n_PCA) 
pca_features = pca.fit_transform(df_Zscore[numeric_columns])

pca_df = pd.DataFrame(data=pca_features, columns=['PC1', 'PC2'])
pca_df['diagnosis'] = df_Zscore["diagnosis"]

# Create the scaled PCA dataframe
pca_df_scaled = pca_df.copy()

scaler_df = pca_df[['PC1', 'PC2']]
scaler = 1 / (scaler_df.max() - scaler_df.min())
 
for index in scaler.index:
    pca_df_scaled[index] *= scaler[index]


fig13 = sns.lmplot(
  x='PC1', 
  y='PC2', 
  data=pca_df_scaled, 
  hue='diagnosis', 
  scatter_kws={'alpha':0.5}, 
  fit_reg=False, 
  legend=False, 
  hue_order=["B", "M"],
  height=5, aspect=1.5
)

# Plot the loadings on a scatterplot
for i, varnames in enumerate(numeric_columns):
    plt.scatter(pca.components_[0][i], pca.components_[1][i], marker = "s", s=200)
    # plt.text(pca.components_[0][i], pca.components_[1][i], varnames,fontsize=10)
# # Define the axes
slope, intercept, r, p, std_err = linregress(pca.components_[0], pca.components_[1])
x = slope * np.linspace(-0.35, 0.35, 10) + intercept
y = np.linspace(-0.35, 0.35, 10)
plt.plot(x, y, color = "tab:red", linestyle='--')

plt.legend(
    ["Linear Regression",
    "B",
    "M",
    "Radius", 
    "Texture", 
    "Perimeter", 
    "Area", 
    "Smoothness", 
    "Compactness", 
    "Concavity", 
    "Concave Points", 
    "Symetry", 
    "Fractal Dimension"],
    title = "Predictor Type", ncol= 1, bbox_to_anchor = (1.05, 1.0), frameon = True, shadow = True)

# # plt.grid("on")
plt.title('PCA - Normalized 2D Projection')
plt.tight_layout()
plt.show()

# fig13.savefig(r"figures/5-2-PCA-2D-scatter-and-loading.pdf")
# fig13.savefig(r"figures/5-2-PCA-2D-scatter-and-loading.png")


n_PCA = 3
pca = PCA(n_components=n_PCA) 
pca_features = pca.fit_transform(df_Zscore[numeric_columns])

pca_df = pd.DataFrame(data=pca_features, columns=['PC1', 'PC2', 'PC3'])
pca_df['diagnosis'] = df_Zscore["diagnosis"]

# Create the scaled PCA dataframe
pca_df_scaled = pca_df.copy()
 
scaler_df = pca_df[['PC1', 'PC2', 'PC3']]
scaler = 1 / (scaler_df.max() - scaler_df.min())
 
for index in scaler.index:
    pca_df_scaled[index] *= scaler[index]

# Initialize the 3D graph
fig14 = plt.figure(figsize=(6,6))
ax = fig14.add_subplot(111, projection='3d')

data_B = pca_df_scaled[pca_df_scaled["diagnosis"]=="B"]
data_M = pca_df_scaled[pca_df_scaled["diagnosis"]=="M"]

ax.scatter3D(data_B['PC1'], data_B['PC2'], data_B['PC3'], color="tab:blue", alpha=0.5)
ax.scatter3D(data_M['PC1'], data_M['PC2'], data_M['PC3'], color="tab:orange", alpha=0.5)

# Plot title of graph
plt.title(f'PCA - Normalized 3D Projection')
 
# Plot x, y, z labels
ax.set_xlabel('Principal component 1', rotation=150)
ax.set_ylabel('Principal component 2')
ax.set_zlabel('Principal component 3', rotation=60)

plt.legend(["B", "M"], loc = 'center', ncol= 2, bbox_to_anchor = (0.9, 0.9), frameon = True, shadow = True)
plt.tight_layout()
plt.show()

# fig14.savefig(r"figures/5-2-PCA-3D-scatter.pdf")
# fig14.savefig(r"figures/5-2-PCA-3D-scatter.png")

	id	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	fractal_dimension_mean	radius_se	texture_se	perimeter_se	area_se	smoothness_se	compactness_se	concavity_se	concave points_se	symmetry_se	fractal_dimension_se	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
564	926424	M	21.56	22.39	142.00	1479.0	0.11100	0.11590	0.24390	0.13890	0.1726	0.05623	1.1760	1.256	7.673	158.70	0.010300	0.02891	0.05198	0.02454	0.01114	0.004239	25.450	26.40	166.10	2027.0	0.14100	0.21130	0.4107	0.2216	0.2060	0.07115
565	926682	M	20.13	28.25	131.20	1261.0	0.09780	0.10340	0.14400	0.09791	0.1752	0.05533	0.7655	2.463	5.203	99.04	0.005769	0.02423	0.03950	0.01678	0.01898	0.002498	23.690	38.25	155.00	1731.0	0.11660	0.19220	0.3215	0.1628	0.2572	0.06637
566	926954	M	16.60	28.08	108.30	858.1	0.08455	0.10230	0.09251	0.05302	0.1590	0.05648	0.4564	1.075	3.425	48.55	0.005903	0.03731	0.04730	0.01557	0.01318	0.003892	18.980	34.12	126.70	1124.0	0.11390	0.30940	0.3403	0.1418	0.2218	0.07820
567	927241	M	20.60	29.33	140.10	1265.0	0.11780	0.27700	0.35140	0.15200	0.2397	0.07016	0.7260	1.595	5.772	86.22	0.006522	0.06158	0.07117	0.01664	0.02324	0.006185	25.740	39.42	184.60	1821.0	0.16500	0.86810	0.9387	0.2650	0.4087	0.12400
568	92751	B	7.76	24.54	47.92	181.0	0.05263	0.04362	0.00000	0.00000	0.1587	0.05884	0.3857	1.428	2.548	19.15	0.007189	0.00466	0.00000	0.00000	0.02676	0.002783	9.456	30.37	59.16	268.6	0.08996	0.06444	0.0000	0.0000	0.2871	0.07039

	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	fractal_dimension_mean	radius_se	texture_se	perimeter_se	area_se	smoothness_se	compactness_se	concavity_se	concave points_se	symmetry_se	fractal_dimension_se	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
0	M	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	0.07871	1.0950	0.9053	8.589	153.40	0.006399	0.04904	0.05373	0.01587	0.03003	0.006193	25.38	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890
1	M	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	0.05667	0.5435	0.7339	3.398	74.08	0.005225	0.01308	0.01860	0.01340	0.01389	0.003532	24.99	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902
2	M	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	0.05999	0.7456	0.7869	4.585	94.03	0.006150	0.04006	0.03832	0.02058	0.02250	0.004571	23.57	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758
3	M	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	0.2597	0.09744	0.4956	1.1560	3.445	27.23	0.009110	0.07458	0.05661	0.01867	0.05963	0.009208	14.91	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300
4	M	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	0.1809	0.05883	0.7572	0.7813	5.438	94.44	0.011490	0.02461	0.05688	0.01885	0.01756	0.005115	22.54	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678

	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	fractal_dimension_mean	radius_se	texture_se	perimeter_se	area_se	smoothness_se	compactness_se	concavity_se	concave points_se	symmetry_se	fractal_dimension_se	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst
count	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000	569.000000
mean	14.127292	19.289649	91.969033	654.889104	0.096360	0.104341	0.088799	0.048919	0.181162	0.062798	0.405172	1.216853	2.866059	40.337079	0.007041	0.025478	0.031894	0.011796	0.020542	0.003795	16.269190	25.677223	107.261213	880.583128	0.132369	0.254265	0.272188	0.114606	0.290076	0.083946
std	3.524049	4.301036	24.298981	351.914129	0.014064	0.052813	0.079720	0.038803	0.027414	0.007060	0.277313	0.551648	2.021855	45.491006	0.003003	0.017908	0.030186	0.006170	0.008266	0.002646	4.833242	6.146258	33.602542	569.356993	0.022832	0.157336	0.208624	0.065732	0.061867	0.018061
min	6.981000	9.710000	43.790000	143.500000	0.052630	0.019380	0.000000	0.000000	0.106000	0.049960	0.111500	0.360200	0.757000	6.802000	0.001713	0.002252	0.000000	0.000000	0.007882	0.000895	7.930000	12.020000	50.410000	185.200000	0.071170	0.027290	0.000000	0.000000	0.156500	0.055040
25%	11.700000	16.170000	75.170000	420.300000	0.086370	0.064920	0.029560	0.020310	0.161900	0.057700	0.232400	0.833900	1.606000	17.850000	0.005169	0.013080	0.015090	0.007638	0.015160	0.002248	13.010000	21.080000	84.110000	515.300000	0.116600	0.147200	0.114500	0.064930	0.250400	0.071460
50%	13.370000	18.840000	86.240000	551.100000	0.095870	0.092630	0.061540	0.033500	0.179200	0.061540	0.324200	1.108000	2.287000	24.530000	0.006380	0.020450	0.025890	0.010930	0.018730	0.003187	14.970000	25.410000	97.660000	686.500000	0.131300	0.211900	0.226700	0.099930	0.282200	0.080040
75%	15.780000	21.800000	104.100000	782.700000	0.105300	0.130400	0.130700	0.074000	0.195700	0.066120	0.478900	1.474000	3.357000	45.190000	0.008146	0.032450	0.042050	0.014710	0.023480	0.004558	18.790000	29.720000	125.400000	1084.000000	0.146000	0.339100	0.382900	0.161400	0.317900	0.092080
max	28.110000	39.280000	188.500000	2501.000000	0.163400	0.345400	0.426800	0.201200	0.304000	0.097440	2.873000	4.885000	21.980000	542.200000	0.031130	0.135400	0.396000	0.052790	0.078950	0.029840	36.040000	49.540000	251.200000	4254.000000	0.222600	1.058000	1.252000	0.291000	0.663800	0.207500

Applied Computational Intelligence - HW1¶

0. Packages and General Options¶

1. Describe your data¶

2. Unconditional mono-variate analysis¶

3. Class-conditional mono-variate analysis of each of the predictors¶

4. Bi-variate analysis of the predictors¶

5. Multi-variate analysis of the predictors¶